$\phi$-divergence? I am frustrated of looking for a  simple explanation of this term $\phi$-divergence, but I cannot find any. Therefore I would be really grateful if somebody could introduce a reference or write a definition (even qualitative for it). Here is the paper that I first noticed the term in:
Jiménez, R., and J. E. Yukich. "Statistical distances based on Euclidean graphs." Recent Advances in Applied Probability. Springer US, 2005. 223-239.
 A: Ok found it myself. It was part of the following paper:
Jiménez-Gamero, María-Dolores, et al. "Minimum $\phi$-divergence estimation in misspecified multinomial models." Computational Statistics & Data Analysis 55.12 (2011): 3365-3378.
$\phi: [0,\infty) \to \mathbb{R}$ is a strictly convex function, twice continuously differentiable in $(0,\infty)$. For arbitrary $Q = (q_1,q_2, ... .,q_m)^t,P = (p_1,p_2, . . . ,p_m)^t ∈ \Delta_m$, the $\phi$-divergence between $Q$ and $P$ is defined by
(Csiszár, 1967)
$$D_\phi(Q,P) =\sum\limits_{i=1}^{m}p_i\phi(\frac{q_i}{p_i}).$$
A: This paper by Love and Bayraksan gives this introduction: '$\phi$-divergences are used in statistics to measure the "distance" between two distributions,' and this formal definition:
$I_{\phi}(p,q) = \sum_{\omega = 1}^{n}{q_\omega\phi(\frac{p_\omega}{q_\omega})}$
where $p, q$ are probability vectors and $\phi$ is a function on $t > 0$. It cites as examples Kullback-Leibler divergence and $\chi^2$ distance. The introduction begins on p. 5, examples given on p. 7.
A: According to Jager and Wellner this term was invented by I. Csiszar (1963), but his paper is in german. Jager and Wellner use it to construct goodness-of-fit tests and they give the following definition:
$K(u,v) = v \phi(\frac{u}{v}) + (1-v)\phi(\frac{1-u}{1-v})$
